By definition, tan^(-1)(4/3) = (theta) means that tan(theta) = 4/3. So draw a right triangle, label the one angle as "theta", and fill in the "opposite" and "adjacent" values. Use the Pythagorean Theorem to find the length of the remaining side. Then take the cosine.

Originally Posted by Byud

2. Find all exact solutions (in simplest form) to the following equations.

a) 2cosxsinx +cosx = 0

How would you start the solution to 2XY + X = 0? Do the same factorization here.

Originally Posted by Byud

b)sin2x = tanx

Convert the left-hand side to sines and cosines, using the double-angle identity they gave you. Convert the right-hand side to sines and cosines using the definition of tangent. See where that leads....

Originally Posted by Byud

I tried on each, and failed miserably on each.

How so? (You might have been "nearly there", but until we can see your work, we just can't know where you're needing the help.)